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I answered the question from 3 to 16 for lab 1: encoding.

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juddin22
2026-03-28 20:36:30 -04:00
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@@ -6,10 +6,6 @@ Create the following variables.
a = Bits("11110000") a = Bits("11110000")
b = Bits("10101010") b = Bits("10101010")
``` ```
print(a)
11110000
print(b)
10101010
For each of the following bytes, give an equivalent For each of the following bytes, give an equivalent
expression which uses only `a`, `b`, and bit operators. expression which uses only `a`, `b`, and bit operators.
@@ -25,16 +21,30 @@ The answers to the first two questions are given.
3. 00000001 3. 00000001
a>>7
4. 10000000 4. 10000000
(a>>7)<<7
5. 01010000 5. 01010000
~b<<4
6. 00001010 6. 00001010
b>>4
7. 01010000 7. 01010000
~b<<4
8. 10101011 8. 10101011
b|(~a>>3)
## Integer questions ## Integer questions
These questions are difficult! Try exploring ideas with `Bits` These questions are difficult! Try exploring ideas with `Bits`
@@ -44,9 +54,13 @@ talk with others.
9. If `a` represents a positive integer, and `one = Bits(1, length=len(a))`, 9. If `a` represents a positive integer, and `one = Bits(1, length=len(a))`,
give an expression equivalent to `-a`, but which does not use negation. give an expression equivalent to `-a`, but which does not use negation.
(~a) + one
10. It is extremely easy to double a binary number: just shift all the bits 10. It is extremely easy to double a binary number: just shift all the bits
to the left. (`a << 1` is twice `a`.) Explain why this trick works. to the left. (`a << 1` is twice `a`.) Explain why this trick works.
a << 1 doubles a because shifting left moves all the bits one place, so each bit’s value doubles.
11. Consider the following: 11. Consider the following:
``` ```
>>> hundred = Bits(100, 8) >>> hundred = Bits(100, 8)
@@ -59,17 +73,28 @@ talk with others.
``` ```
Apparently 100 + 100 = -56. What's going on here? Apparently 100 + 100 = -56. What's going on here?
100 + 100 = 200, but we only have 8 bits, which can’t hold 200, so it becomes a negative number.
12. What is the bit representation of negative zero? Explain your answer. 12. What is the bit representation of negative zero? Explain your answer.
Negative zero is 00000000 because flipping zero and adding 1 is still zero.
13. What's the largest integer that can be represented in a single byte? 13. What's the largest integer that can be represented in a single byte?
Explain your reasoning. Explain your reasoning.
The largest integer that can be represented in a single byte is 127 because the first bit is 0 (positive) and the other 7 bits are all 1, which makes the biggest number possible.I also checked this in the terminal using
largest = Bits("01111111"), print(largest.int).
14. What's the smallest integer that can be represented in a single byte? 14. What's the smallest integer that can be represented in a single byte?
Explain your reasoning. Explain your reasoning.
The smallest integer that can be represented in a single byte is -128 because the first bit is 1 (negative) and the other 7 bits are all 0.
15. What's the largest integer that can be represented in `n` bits? 15. What's the largest integer that can be represented in `n` bits?
Explain your reasoning. Explain your reasoning.
The largest integer that can be represented in n bits is when the first bit is 0 (positive) and all the other bits are 1. This makes the biggest number possible with n bits.
## Text questions ## Text questions
16. Look at the bits for a few different characters using the `utf8` encoding. 16. Look at the bits for a few different characters using the `utf8` encoding.
@@ -94,4 +119,5 @@ talk with others.
Make a hypothesis about how this could work. Make a hypothesis about how this could work.
The decoder knows how many bits to read by looking at the first bits. The pattern at the start tells it if the character is 1, 2, 3, or 4 bytes long.